Artist Tino Sehgal with participants in These Associations, his performance piece now at Tate Modern's Turbine Hall. Photograph: Johnny Green/Tate Modern

Unilever has ended its sponsorship of Tate Modern's Turbine Hall annual commission that has produced some of the London gallery's most memorable exhibitions.

Tino Sehgal's These Associations, the first live performance piece in the former Bankside power station, will be the final work in the Unilever-sponsored series, which has attracted almost 30 million visitors over the past dozen years.

The £4.4m sponsorship deal with Unilever, has led to 13 commissions, including Bruce Nauman's soundscapes, Olafur Eliasson's huge, yellow, artificial indoor sun The Weather Project in 2003-04, which saw visitors stretch out on the floor of the vast space to bask in its glow, and Doris Salcedo's Shibboleth in 2007, which featured a crack running the length of the hall. Some commissions have been acquired for the gallery's permanent collection, including the Chinese artist Ai Weiwei's Sunflower Seeds, although it bought only a tenth of the 100m porcelain seeds, all individually sculpted and painted by Chinese craft workers, shown in the 2010 exhibition.

The current show, in which participants stop and engage visitors with intimate, personal stories, closes on 28 October.

The Turbine Hall is due to temporarily close next year to enable construction of the gallery's Herzog & de Meuron-designed extension. The project, which is planned to cost £215m in total, is due for completion by 2016 – delayed from its previously projected opening of this year.

The first phase of the extension, the £90m performance art and video installation space called the Tanks, opened in July.

A spokeswoman for Tate said: "Due to the building works at Tate Modern, there will not be a Turbine Hall commission in 2013. We will start discussions with other companies about the sponsorship of the Turbine Hall commission from 2014 onwards."

Unilever, whose brands include Pot Noodle and PG Tips, will continue as a corporate member of Tate. But the company said it is planning a change of direction in its sponsorship programme, which is more focused on sustainability and the environment.

"While we will continue our relationship with Tate as a corporate member, we are now planning a change of direction which will fit closely with our company's mission to double the size of our business while reducing our environmental impact and increasing our positive social impact.

Other prominent Tate sponsors include Bloomberg, the business and financial news organisation, and, more controversially, the oil company BP. The Tate received £45.1m in public funding last year, and raised an additional £67.9m. Its 100,000 members contribute about £3m per year.